Question

If a, b, c, and d are integers such that $a + b + c + d = 30$, then the minimum possible value of $(a - b)^2 + (a - c)^2 + (a - d)^2$ is

• A. 5
• B. 2
• C. 1
• D. 4

Answer 1

Answer: (B)

2

Answer 2

The expression $a+b+c+d=30$, where $a,b,c,d$ are integers.
To maximize the value of $(a−b)^2+(a−c)^2+(a−d)^2$, each bracket should have the least possible value.

Choosing the values $(a,b,c,d)=(8,8,7,7),$ the given expression evaluates to 2, and it cannot have a smaller value.